Cell phone in Taiwan and China

I am traveling to Taiwan and China for six weeks. I'm arriving in Taipei is there a cellphone I can buy at the airport in Taipei that I can also use during my time in China? How much should I expect to spend?
Thank you!

If you don't want to use roaming and pay international rates, you can buy a chip from CHT the mobile service provider in Taiwan. When you go to Mainland China get a chip from one of the two main service providers there. GSM signals are used in both Taiwan and Mainland China.